Calculating IQR from stem leaf plots with Odd number of scores with step by step illustration

1. - Mr Kim

2. Finding IQR for odd number of scores

3. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

4. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
First, find the Median by
crossing off the scores

5. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
**Make sure the scores
are in Ascending Order
first!

6. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
**Make sure the scores
are in Ascending Order
first!

7. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
**Make sure the scores
are in Ascending Order
first!
The scores here go
from Small to Big

8. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7 The scores here go
from Small to Big
**Make sure the scores
are in Ascending Order
first!

9. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7 The scores here go
from Small to Big
**Make sure the scores
are in Ascending Order
first!

10. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7 The scores here go
from Small to Big
**Make sure the scores
are in Ascending Order
first!

11. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7 The scores here go
from Small to Big
**Make sure the scores
are in Ascending Order
first!

12. 1 5 3 5 8 5 9
2 3 0 1 3
3 2 7 4
4 2 6
5 1 7
For example this is not
in ascending order

13. 1 5 3 5 8 5 9
2 3 0 1 3
3 2 7 4
4 2 6
5 1 7
For example this is not
in ascending order

14. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now, start by crossing
off the Smallest Number

15. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
13
Now, start by crossing
off the Smallest Number

16. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

17. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now cross off the
Biggest Number

18. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
57
Now cross off the
Biggest Number

19. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

20. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Cross off the scores in
the directions shown

21. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

22. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

23. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

24. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

25. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

26. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

27. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

28. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

29. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

30. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

31. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

32. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

33. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

34. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

35. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Stop here

36. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Always stop at “Out”

37. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
So the Median (Q2)
is…

38. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
So the Median (Q2) is
21

39. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now put 2 lines
around it like shown

40. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now find the Lower and
Upper Quartile by dividing
the Stem-Leaf Plot in two

41. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
**It is very important to
divide the sides properly

42. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
To do this, count the
scores from the start
until you reach the Line

43. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

44. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

45. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

46. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

47. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

48. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

49. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

50. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

51. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Stop here!

52. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now put a Border around
the scores that you just
counted

53. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

54. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now put a Border around
the other side

55. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

56. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
This is how you correctly
divide the sides

57. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now find the Median for
both sides of the scores
by crossing off each side
at a time

58. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
We will start with
this side

59. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Remember the
directions

60. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

61. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

62. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

63. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

64. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“In”

65. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
“Out”

66. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Stop here!

67. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7

68. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18

69. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18
So the Lower Quartile (Q1)
is between 15 and 18
which is…

70. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18
So the Lower Quartile (Q1)
is between 15 and 18
which is…
15

71. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18
So the Lower Quartile (Q1)
is between 15 and 18
which is…
1815

72. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18
So the Lower Quartile (Q1)
is between 15 and 18
which is…
2
1815 

73. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18
So the Lower Quartile (Q1)
is between 15 and 18
which is…
5.16
2
1815



74. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
15
18
So the Lower Quartile (Q1)
is between 15 and 18
which is 16.5

75. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5

76. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Now cross off the
other side
Lower Quartile:
16.5

77. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
Remember the
directions

78. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
“In”

79. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
“Out”

80. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
“In”

81. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
“Out”

82. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
“In”

83. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
“Out”

84. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
Stop here!

85. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5

86. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
37
42

87. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
So the Upper Quartile (Q3)
is between 37 and 42
which is …37
42

88. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
42
So the Upper Quartile (Q3)
is between 37 and 42
which is …37
37

89. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
42
So the Upper Quartile (Q3)
is between 37 and 42
which is …37
4237 

90. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
42
So the Upper Quartile (Q3)
is between 37 and 42
which is …37
2
4237 

91. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
42
So the Upper Quartile (Q3)
is between 37 and 42
which is …37
5.39
2
4237



92. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
42
So the Upper Quartile (Q3)
is between 37 and 42
which is 39.537

93. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
Upper Quartile:
39.5

94. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
So, the Interquartile Range is
Upper Quartile:
39.5

95. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
So, the Interquartile Range is
Upper Quartile:
39.5

96. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
Upper Quartile:
39.5
So, the Interquartile Range is
39.5 –

97. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
Upper Quartile:
39.5
So, the Interquartile Range is
39.5 –

98. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
Upper Quartile:
39.5
So, the Interquartile Range is
39.5 – 16.5

99. 1 3 5 5 5 8 9
2 0 1 1 3
3 2 4 7
4 2 6
5 1 7
Lower Quartile:
16.5
So, the Interquartile Range is
39.5 – 16.5 = 23
Our Final Answer!
Upper Quartile:
39.5